Transition Charts and Exceptional Factors A Second Elimination Chart for Endpoint-Compression Word Fibers

This preprint studies transition charts for endpoint-compression word fibers in PGL2(R)\mathrm{PGL}_2(\mathbb R)PGL2(R). Building on the generic rational fiber chart of GMA6, it constructs a second elimination chart that recovers the generic part of the coordinate boundary $\Delta =0$. The main result identifies a universal transition factor separating image-side degenerations, $(u-1)(uv-w)$, from tail-side word-internal factors. The length-four case is shown to close as a two-chart rational curve, while higher-length global cover and embedded-component questions are left as explicit open problems. Symbolic verification scripts check the transition identities, branch selection, pole coprimality, and low-length factor tables.